Page 135 - Power Electronic Control in Electrical Systems

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Power electronic control in electrical systems 123

Fig. 4.11 Nominal representation of the transmission line.

Fig. 4.12 Circuit representation of tap-changing transformer.

In power flow studies, the transformer is normally represented only by its leakage
reactance X t , i.e. the resistance is neglected. The p-circuit shown in Figure 4.12 is used
to derive the transfer admittance of a transformer with off-nominal tap setting T:1.
" #
1 T
I l jX t jX t V l
ˆ T T 2 (4:29)
I m V m
jX t jX t
Series compensation is represented by a capacitive reactance X c connected between
nodes l and m, as shown in Figure 4.13. The transfer admittance of the series capacitor is,
" #
1 1

I l jX c jX c V l
ˆ 1 1 (4:30)
I m V m
jX c jX c
By way of example, the nodal admittance matrix of the three-node network shown in
Figure 4.14 is given as
2 3
1 T

2 3 0 2 3
I 1 jX t jX t 7 V 1
6
6 T T 2 1 jB c 1 7 (4:31)
4 I 2 5 ˆ 6 ‡ ‡ 7 V 2 5
4
jX t jX t R ‡ jX l 2 R ‡ jX l
4 5
I 3 1 1 1 V 3
0 ‡ jB c
R ‡ jX l R ‡ jX l 2 jX c